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Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, e, l
from proveit.numbers import Add, Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = ExprTuple(sub_expr1, Add(frac(one, Exp(e, two)), sub_expr1))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}, \frac{1}{e^{2}} + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple4, 1
1Operationoperator: 35
operands: 2
2ExprTuple3, 4
3Operationoperator: 15
operands: 5
4Operationoperator: 6
operand: 9
5ExprTuple41, 8
6Literal
7ExprTuple9
8Operationoperator: 31
operands: 10
9Lambdaparameter: 24
body: 12
10ExprTuple29, 33
11ExprTuple24
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple41, 19
17Literal
18ExprTuple24, 20
19Operationoperator: 31
operands: 21
20Operationoperator: 22
operands: 23
21ExprTuple24, 33
22Literal
23ExprTuple25, 26
24Variable
25Operationoperator: 35
operands: 27
26Operationoperator: 35
operands: 28
27ExprTuple29, 41
28ExprTuple30, 38
29Variable
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Literal
34Operationoperator: 35
operands: 36
35Literal
36ExprTuple37, 38
37Literal
38Operationoperator: 39
operand: 41
39Literal
40ExprTuple41
41Literal